LMFDB - Dirichlet character orbit 160083.sx

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(160083, base_ring=CyclotomicField(6930)) M = H._module chi = DirichletCharacter(H, M([1925,4785,4662])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,160083)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$160083$
Conductor:	$160083$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$6930$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{3465})$
Fixed field:	Number field defined by a degree 6930 polynomial (not computed)

First 14 of 1440 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{160083}(5,\cdot)$	$1$	$1$	$e\left(\frac{6257}{6930}\right)$	$e\left(\frac{2792}{3465}\right)$	$e\left(\frac{674}{3465}\right)$	$e\left(\frac{1637}{2310}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{6607}{6930}\right)$	$e\left(\frac{2119}{3465}\right)$	$e\left(\frac{151}{385}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{1}{3465}\right)$
$\chi_{160083}(38,\cdot)$	$1$	$1$	$e\left(\frac{1717}{6930}\right)$	$e\left(\frac{1717}{3465}\right)$	$e\left(\frac{829}{3465}\right)$	$e\left(\frac{1717}{2310}\right)$	$e\left(\frac{75}{154}\right)$	$e\left(\frac{5777}{6930}\right)$	$e\left(\frac{3434}{3465}\right)$	$e\left(\frac{216}{385}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{2546}{3465}\right)$
$\chi_{160083}(257,\cdot)$	$1$	$1$	$e\left(\frac{1571}{6930}\right)$	$e\left(\frac{1571}{3465}\right)$	$e\left(\frac{1037}{3465}\right)$	$e\left(\frac{1571}{2310}\right)$	$e\left(\frac{81}{154}\right)$	$e\left(\frac{6541}{6930}\right)$	$e\left(\frac{3142}{3465}\right)$	$e\left(\frac{338}{385}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{2608}{3465}\right)$
$\chi_{160083}(290,\cdot)$	$1$	$1$	$e\left(\frac{2881}{6930}\right)$	$e\left(\frac{2881}{3465}\right)$	$e\left(\frac{832}{3465}\right)$	$e\left(\frac{571}{2310}\right)$	$e\left(\frac{101}{154}\right)$	$e\left(\frac{6521}{6930}\right)$	$e\left(\frac{2297}{3465}\right)$	$e\left(\frac{103}{385}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{248}{3465}\right)$
$\chi_{160083}(383,\cdot)$	$1$	$1$	$e\left(\frac{1433}{6930}\right)$	$e\left(\frac{1433}{3465}\right)$	$e\left(\frac{1376}{3465}\right)$	$e\left(\frac{1433}{2310}\right)$	$e\left(\frac{93}{154}\right)$	$e\left(\frac{523}{6930}\right)$	$e\left(\frac{2866}{3465}\right)$	$e\left(\frac{274}{385}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{2809}{3465}\right)$
$\chi_{160083}(416,\cdot)$	$1$	$1$	$e\left(\frac{4093}{6930}\right)$	$e\left(\frac{628}{3465}\right)$	$e\left(\frac{1621}{3465}\right)$	$e\left(\frac{1783}{2310}\right)$	$e\left(\frac{9}{154}\right)$	$e\left(\frac{1223}{6930}\right)$	$e\left(\frac{1256}{3465}\right)$	$e\left(\frac{29}{385}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{2249}{3465}\right)$
$\chi_{160083}(542,\cdot)$	$1$	$1$	$e\left(\frac{5809}{6930}\right)$	$e\left(\frac{2344}{3465}\right)$	$e\left(\frac{268}{3465}\right)$	$e\left(\frac{1189}{2310}\right)$	$e\left(\frac{141}{154}\right)$	$e\left(\frac{5249}{6930}\right)$	$e\left(\frac{1223}{3465}\right)$	$e\left(\frac{172}{385}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{2612}{3465}\right)$
$\chi_{160083}(698,\cdot)$	$1$	$1$	$e\left(\frac{17}{6930}\right)$	$e\left(\frac{17}{3465}\right)$	$e\left(\frac{2444}{3465}\right)$	$e\left(\frac{17}{2310}\right)$	$e\left(\frac{109}{154}\right)$	$e\left(\frac{2047}{6930}\right)$	$e\left(\frac{34}{3465}\right)$	$e\left(\frac{86}{385}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{2461}{3465}\right)$
$\chi_{160083}(731,\cdot)$	$1$	$1$	$e\left(\frac{6367}{6930}\right)$	$e\left(\frac{2902}{3465}\right)$	$e\left(\frac{1609}{3465}\right)$	$e\left(\frac{1747}{2310}\right)$	$e\left(\frac{59}{154}\right)$	$e\left(\frac{5177}{6930}\right)$	$e\left(\frac{2339}{3465}\right)$	$e\left(\frac{96}{385}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{1046}{3465}\right)$
$\chi_{160083}(983,\cdot)$	$1$	$1$	$e\left(\frac{5641}{6930}\right)$	$e\left(\frac{2176}{3465}\right)$	$e\left(\frac{982}{3465}\right)$	$e\left(\frac{1021}{2310}\right)$	$e\left(\frac{15}{154}\right)$	$e\left(\frac{2141}{6930}\right)$	$e\left(\frac{887}{3465}\right)$	$e\left(\frac{228}{385}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{3158}{3465}\right)$
$\chi_{160083}(1076,\cdot)$	$1$	$1$	$e\left(\frac{863}{6930}\right)$	$e\left(\frac{863}{3465}\right)$	$e\left(\frac{1571}{3465}\right)$	$e\left(\frac{863}{2310}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{373}{6930}\right)$	$e\left(\frac{1726}{3465}\right)$	$e\left(\frac{244}{385}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{2434}{3465}\right)$
$\chi_{160083}(1202,\cdot)$	$1$	$1$	$e\left(\frac{6899}{6930}\right)$	$e\left(\frac{3434}{3465}\right)$	$e\left(\frac{1658}{3465}\right)$	$e\left(\frac{2279}{2310}\right)$	$e\left(\frac{73}{154}\right)$	$e\left(\frac{1159}{6930}\right)$	$e\left(\frac{3403}{3465}\right)$	$e\left(\frac{47}{385}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{1627}{3465}\right)$
$\chi_{160083}(1235,\cdot)$	$1$	$1$	$e\left(\frac{5419}{6930}\right)$	$e\left(\frac{1954}{3465}\right)$	$e\left(\frac{1678}{3465}\right)$	$e\left(\frac{799}{2310}\right)$	$e\left(\frac{41}{154}\right)$	$e\left(\frac{1499}{6930}\right)$	$e\left(\frac{443}{3465}\right)$	$e\left(\frac{192}{385}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{167}{3465}\right)$
$\chi_{160083}(1424,\cdot)$	$1$	$1$	$e\left(\frac{4087}{6930}\right)$	$e\left(\frac{622}{3465}\right)$	$e\left(\frac{2389}{3465}\right)$	$e\left(\frac{1777}{2310}\right)$	$e\left(\frac{43}{154}\right)$	$e\left(\frac{4577}{6930}\right)$	$e\left(\frac{1244}{3465}\right)$	$e\left(\frac{361}{385}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{3011}{3465}\right)$

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Elliptic curves over $\Q$
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Character	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{160083}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6257}{6930}\right)\)	\(e\left(\frac{2792}{3465}\right)\)	\(e\left(\frac{674}{3465}\right)\)	\(e\left(\frac{1637}{2310}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{6607}{6930}\right)\)	\(e\left(\frac{2119}{3465}\right)\)	\(e\left(\frac{151}{385}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{1}{3465}\right)\)
\(\chi_{160083}(38,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1717}{6930}\right)\)	\(e\left(\frac{1717}{3465}\right)\)	\(e\left(\frac{829}{3465}\right)\)	\(e\left(\frac{1717}{2310}\right)\)	\(e\left(\frac{75}{154}\right)\)	\(e\left(\frac{5777}{6930}\right)\)	\(e\left(\frac{3434}{3465}\right)\)	\(e\left(\frac{216}{385}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{2546}{3465}\right)\)
\(\chi_{160083}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1571}{6930}\right)\)	\(e\left(\frac{1571}{3465}\right)\)	\(e\left(\frac{1037}{3465}\right)\)	\(e\left(\frac{1571}{2310}\right)\)	\(e\left(\frac{81}{154}\right)\)	\(e\left(\frac{6541}{6930}\right)\)	\(e\left(\frac{3142}{3465}\right)\)	\(e\left(\frac{338}{385}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{2608}{3465}\right)\)
\(\chi_{160083}(290,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2881}{6930}\right)\)	\(e\left(\frac{2881}{3465}\right)\)	\(e\left(\frac{832}{3465}\right)\)	\(e\left(\frac{571}{2310}\right)\)	\(e\left(\frac{101}{154}\right)\)	\(e\left(\frac{6521}{6930}\right)\)	\(e\left(\frac{2297}{3465}\right)\)	\(e\left(\frac{103}{385}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{248}{3465}\right)\)
\(\chi_{160083}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1433}{6930}\right)\)	\(e\left(\frac{1433}{3465}\right)\)	\(e\left(\frac{1376}{3465}\right)\)	\(e\left(\frac{1433}{2310}\right)\)	\(e\left(\frac{93}{154}\right)\)	\(e\left(\frac{523}{6930}\right)\)	\(e\left(\frac{2866}{3465}\right)\)	\(e\left(\frac{274}{385}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{2809}{3465}\right)\)
\(\chi_{160083}(416,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4093}{6930}\right)\)	\(e\left(\frac{628}{3465}\right)\)	\(e\left(\frac{1621}{3465}\right)\)	\(e\left(\frac{1783}{2310}\right)\)	\(e\left(\frac{9}{154}\right)\)	\(e\left(\frac{1223}{6930}\right)\)	\(e\left(\frac{1256}{3465}\right)\)	\(e\left(\frac{29}{385}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{2249}{3465}\right)\)
\(\chi_{160083}(542,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5809}{6930}\right)\)	\(e\left(\frac{2344}{3465}\right)\)	\(e\left(\frac{268}{3465}\right)\)	\(e\left(\frac{1189}{2310}\right)\)	\(e\left(\frac{141}{154}\right)\)	\(e\left(\frac{5249}{6930}\right)\)	\(e\left(\frac{1223}{3465}\right)\)	\(e\left(\frac{172}{385}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{2612}{3465}\right)\)
\(\chi_{160083}(698,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{6930}\right)\)	\(e\left(\frac{17}{3465}\right)\)	\(e\left(\frac{2444}{3465}\right)\)	\(e\left(\frac{17}{2310}\right)\)	\(e\left(\frac{109}{154}\right)\)	\(e\left(\frac{2047}{6930}\right)\)	\(e\left(\frac{34}{3465}\right)\)	\(e\left(\frac{86}{385}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{2461}{3465}\right)\)
\(\chi_{160083}(731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6367}{6930}\right)\)	\(e\left(\frac{2902}{3465}\right)\)	\(e\left(\frac{1609}{3465}\right)\)	\(e\left(\frac{1747}{2310}\right)\)	\(e\left(\frac{59}{154}\right)\)	\(e\left(\frac{5177}{6930}\right)\)	\(e\left(\frac{2339}{3465}\right)\)	\(e\left(\frac{96}{385}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{1046}{3465}\right)\)
\(\chi_{160083}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5641}{6930}\right)\)	\(e\left(\frac{2176}{3465}\right)\)	\(e\left(\frac{982}{3465}\right)\)	\(e\left(\frac{1021}{2310}\right)\)	\(e\left(\frac{15}{154}\right)\)	\(e\left(\frac{2141}{6930}\right)\)	\(e\left(\frac{887}{3465}\right)\)	\(e\left(\frac{228}{385}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{3158}{3465}\right)\)
\(\chi_{160083}(1076,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{863}{6930}\right)\)	\(e\left(\frac{863}{3465}\right)\)	\(e\left(\frac{1571}{3465}\right)\)	\(e\left(\frac{863}{2310}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{373}{6930}\right)\)	\(e\left(\frac{1726}{3465}\right)\)	\(e\left(\frac{244}{385}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{2434}{3465}\right)\)
\(\chi_{160083}(1202,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6899}{6930}\right)\)	\(e\left(\frac{3434}{3465}\right)\)	\(e\left(\frac{1658}{3465}\right)\)	\(e\left(\frac{2279}{2310}\right)\)	\(e\left(\frac{73}{154}\right)\)	\(e\left(\frac{1159}{6930}\right)\)	\(e\left(\frac{3403}{3465}\right)\)	\(e\left(\frac{47}{385}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{1627}{3465}\right)\)
\(\chi_{160083}(1235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5419}{6930}\right)\)	\(e\left(\frac{1954}{3465}\right)\)	\(e\left(\frac{1678}{3465}\right)\)	\(e\left(\frac{799}{2310}\right)\)	\(e\left(\frac{41}{154}\right)\)	\(e\left(\frac{1499}{6930}\right)\)	\(e\left(\frac{443}{3465}\right)\)	\(e\left(\frac{192}{385}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{167}{3465}\right)\)
\(\chi_{160083}(1424,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4087}{6930}\right)\)	\(e\left(\frac{622}{3465}\right)\)	\(e\left(\frac{2389}{3465}\right)\)	\(e\left(\frac{1777}{2310}\right)\)	\(e\left(\frac{43}{154}\right)\)	\(e\left(\frac{4577}{6930}\right)\)	\(e\left(\frac{1244}{3465}\right)\)	\(e\left(\frac{361}{385}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{3011}{3465}\right)\)

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First 14 of 1440 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	160083.sx
Modulus	$160083$
Conductor	$160083$
Order	$6930$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(160083\)
Conductor:	\(160083\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(6930\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)